Related papers: Identifying logarithmic tracts
We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerative. Also, we use Bott formula on the Kontsevich space to…
We provide the full theory of thermodynamic formalism for a very general collection of entire functions in class $\mathcal B$. This class overlaps with the collection of all entire functions for which thermodynamic formalism has been so far…
We describe the scheme of jumping lines of logarithmic vector bundles on the projective plane. This result is already proved by Dolgachev and Kapranov when the first Chern class is even, it is new when the first Chern class is odd.
We prove that the group of rational points of a non-isotrivial elliptic curve defined over the perfect closure of a function field in one variable over a finite field is finiteley generated.
Given a real algebraic curve in the projective 3-space, its hyperbolicity locus is the set of lines with respect to which the curve is hyperbolic. We give an example of a smooth irreducible curve whose hyperbolicity locus is disconnected…
In this paper, we evaluate the following families of definite integrals in closed form and we show that they are expressible only in terms of the dilogarithm function and the inverse tangent integral, and elementary functions.…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…
We prove that on a closed surface of genus $g$, the cardinality of a set of simple closed curves in which any two are non-homotopic and intersect at most once is $\lesssim g^2 \log(g)$. This bound matches the largest known constructions to…
Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple,…
We establish that the sequences formed by logarithms and by "fractional" powers of integers, as well as the sequence of prime numbers, are non-holonomic, thereby answering three open problems of Gerhold [Electronic Journal of Combinatorics…
We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack.…
In this note, we consider rational cuspidal plane curves having exactly one cusp whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal embedded…
The {\em spectrum} of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this paper we show that when restricted to using only two variables, but allowing counting quantifiers, the…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…
In this paper, we introduce a variant of the Lambek calculus allowing empty antecedents. This variant uses two connecives: the left division and a unary modality that occurs only with negative polarity and allows weakening in antecedents of…
We consider integrals over vanishing cycles in the Milnor fibration of an isolated singularity defined by a Newton non-degenerate function. We single out a condition where the leading logarithmic term of the expansion of the integral into a…
The signature transform, which is defined in terms of iterated path integrals of all orders, provides a faithful representation of the group of tree-reduced geometric rough paths. While the signature coefficients are known to decay…
We show that every nontrivial finite or infinite connected directed graph with loops and at least one vertex without a loop is uniquely representable as a Cartesian or weak Cartesian product of prime graphs. For finite graphs the…
In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.